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International Journal of Theoretical Physics

, Volume 57, Issue 5, pp 1597–1603 | Cite as

New Constructions of Orthogonal Product Basis Quantum States

  • Huijuan Zuo
  • Shuxia Liu
  • Yinghui Yang
Article

Abstract

An orthogonal basis \({\mathcal {B}}_{9}\) for the Hilbert space C3 × C3 was presented by Bennett et al. (Phys. Rev. A 59, 1070, 1999) which was illustrated in a visual figure in their report. The character of the construction is that each base vector is a product state, thus any distinguishing operator cannot create entanglement. In this paper, we mainly focus on some new constructions of orthogonal product basis quantum states in the high-dimensional quantum systems. Especially, as for the quantum system of (2m + 1) ⊗ (2m + 1), where mZ and m ≥ 2, we have provided the direct construction in mathematical method.

Keywords

New constructions Orthogonal product basis Hadamard matrix High-dimensional quantum systems 

Notes

Acknowledgements

This work is supported by NSFC (Grant Nos. 61402148,61601171), Natural Science Foundation of Hebei Province (F2015205114), Doctoral Scientific Fund Project of Hebei Normal University (F2016B05).

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Copyright information

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Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceHebei Normal UniversityShijiazhuangChina
  2. 2.School of Mathematics and Information ScienceHenan Polytechnic UniversityJiaozuoChina

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